A novel concept of quaternionic fuzzy sets (QFSs) is presented in this paper. QFSs are a generalization traditional and complex based on quaternions. The novelty that the range membership function set quaternions with modulus less than or equal to one, which real imaginary parts can be used for four different features. discussion made intuitive interpretation quaternion-valued grades possible a...

The second quantization of the quaternionic fermionic field is undertaken using real Hilbert space approach to quantum mechanics ([Formula: see text]QM). solution responds an open problem theory, and launches basis development interaction theory.

We prove a Nullstellensatz for the ring of polynomial functions in n non-commuting variables over Hamilton's real quaternions. also characterize generalized identities which hold quaternions, and more generally, any division algebra .

~omplex analyticity is generalized to hypercomplex functions, quaternion or octonion, in such a manner that it’ includes the standard complex definition and does not reduce analytic functions to a trivial class. A brief comparison with other definitions is presented. @ 2003 Elsevier Ltd. All rights reserved. Keywords-&uaternions, Analytic functions, Differential operators.